Phase transitions typically occur in combinatorial computational problems and have important consequences, especially with the current spread of statistical relational learning as well as sequence learning methodologies. In Phase Transitions in Machine Learning the authors begin by describing in detail this phenomenon, and the extensive experimental investigation that supports its presence. They then turn their attention to the possible implications and explore appropriate methods for tackling them. Weaving together fundamental aspects of computer science, statistical physics and machine learning, the book provides sufficient mathematics and physics background to make the subject intelligible to researchers in AI and other computer science communities. Open research issues are also discussed, suggesting promising directions for future research.
Antoine Cornuejols is Full Professor of Computer Science at the AgroParisTech Engineering School in Paris. Attilio Giordana is Full Professor of Computer Science at the University of Piemonte Orientale in Italy. Lorenza Saitta is a Full Professor of Computer Science at the University of Piemonte Orientale in Italy.
Preface; Acknowledgements; Notation; 1. Introduction; 2. Statistical physics and phase transitions; 3. The satisfiability problem; 4. Constraint satisfaction problems; 5. Machine learning; 6. Searching the hypothesis space; 7. Statistical physics and machine learning; 8. Learning, SAT, and CSP; 9. Phase transition in FOL covering test; 10. Phase transitions and relational learning; 11. Phase transitions in grammatical inference; 12. Phase transitions in complex systems; 13. Phase transitions in natural systems; 14. Discussions and open issues; Appendix A. Phase transitions detected in two real cases; Appendix B. An intriguing idea; References; Index.